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Probability Theory
course content

Course Content

Probability Theory

Probability Theory

1. Learn Basic Rules
Random VariableBernoulli Trial 1/2Bernoulli Trial 2/2Binomial Probability 1/2Binomial probability 2/2
2. Probabilities of Several Events
Add ProbabilitiesCalculate Connected ProbabilitiesChallengeMultiply probabilitiesDependent probabilitiesLaw of Total ProbabilityBayes Theorem Challenge
3. Conducting Fascinating Experiments
The First ExperimentThe Second ExperimentThe Third ExperimentCombine Your Knowledge
4. Discrete Distributions
Discrete Uniform DistributionCalculate Fascinating ProbabilityBernoulli DistributionBinomial DistributionChallengePoisson DistributionChallenge
5. Normal Distribution
Normal DistributionChallenge 1Сhallenge 2

Combine Your Knowledge

It is time to deal with three experiments; they are very similar, so firstly, let's recall some theory.

FunctionExplanation
binom.pmf(k, n, p)Calculate the probability to archive exactly k successes among n trials with the probability of success p
binom.sf(k, n, p)Calculate the probability to archive k or more successes among n trials with the probability of success p
binom.cdf(k, n, p)Calculate the probability to archive k or less successes among n trials with the probability of success p

Task

Here, it would be best if we coped with several tasks.

  1. Calculate the probability that among 50 unique pictures, exactly 5 have a defect; the probability that a picture has a defect is 25%.
  2. Calculate the probability that at least 9(9 or more) employees are satisfied with their salary if we know that there are 20 workers in the project. The probability for the positive answer is 75% .
  3. Calculate the probability that 6 or fewer thefts this month will be revealed; we know that in the specific city, the amount of thefts is 10. The probability of revealing is 5%.

Task

Here, it would be best if we coped with several tasks.

  1. Calculate the probability that among 50 unique pictures, exactly 5 have a defect; the probability that a picture has a defect is 25%.
  2. Calculate the probability that at least 9(9 or more) employees are satisfied with their salary if we know that there are 20 workers in the project. The probability for the positive answer is 75% .
  3. Calculate the probability that 6 or fewer thefts this month will be revealed; we know that in the specific city, the amount of thefts is 10. The probability of revealing is 5%.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

Section 3. Chapter 4
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Combine Your Knowledge

It is time to deal with three experiments; they are very similar, so firstly, let's recall some theory.

FunctionExplanation
binom.pmf(k, n, p)Calculate the probability to archive exactly k successes among n trials with the probability of success p
binom.sf(k, n, p)Calculate the probability to archive k or more successes among n trials with the probability of success p
binom.cdf(k, n, p)Calculate the probability to archive k or less successes among n trials with the probability of success p

Task

Here, it would be best if we coped with several tasks.

  1. Calculate the probability that among 50 unique pictures, exactly 5 have a defect; the probability that a picture has a defect is 25%.
  2. Calculate the probability that at least 9(9 or more) employees are satisfied with their salary if we know that there are 20 workers in the project. The probability for the positive answer is 75% .
  3. Calculate the probability that 6 or fewer thefts this month will be revealed; we know that in the specific city, the amount of thefts is 10. The probability of revealing is 5%.

Task

Here, it would be best if we coped with several tasks.

  1. Calculate the probability that among 50 unique pictures, exactly 5 have a defect; the probability that a picture has a defect is 25%.
  2. Calculate the probability that at least 9(9 or more) employees are satisfied with their salary if we know that there are 20 workers in the project. The probability for the positive answer is 75% .
  3. Calculate the probability that 6 or fewer thefts this month will be revealed; we know that in the specific city, the amount of thefts is 10. The probability of revealing is 5%.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

Section 3. Chapter 4
toggle bottom row

Combine Your Knowledge

It is time to deal with three experiments; they are very similar, so firstly, let's recall some theory.

FunctionExplanation
binom.pmf(k, n, p)Calculate the probability to archive exactly k successes among n trials with the probability of success p
binom.sf(k, n, p)Calculate the probability to archive k or more successes among n trials with the probability of success p
binom.cdf(k, n, p)Calculate the probability to archive k or less successes among n trials with the probability of success p

Task

Here, it would be best if we coped with several tasks.

  1. Calculate the probability that among 50 unique pictures, exactly 5 have a defect; the probability that a picture has a defect is 25%.
  2. Calculate the probability that at least 9(9 or more) employees are satisfied with their salary if we know that there are 20 workers in the project. The probability for the positive answer is 75% .
  3. Calculate the probability that 6 or fewer thefts this month will be revealed; we know that in the specific city, the amount of thefts is 10. The probability of revealing is 5%.

Task

Here, it would be best if we coped with several tasks.

  1. Calculate the probability that among 50 unique pictures, exactly 5 have a defect; the probability that a picture has a defect is 25%.
  2. Calculate the probability that at least 9(9 or more) employees are satisfied with their salary if we know that there are 20 workers in the project. The probability for the positive answer is 75% .
  3. Calculate the probability that 6 or fewer thefts this month will be revealed; we know that in the specific city, the amount of thefts is 10. The probability of revealing is 5%.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

It is time to deal with three experiments; they are very similar, so firstly, let's recall some theory.

FunctionExplanation
binom.pmf(k, n, p)Calculate the probability to archive exactly k successes among n trials with the probability of success p
binom.sf(k, n, p)Calculate the probability to archive k or more successes among n trials with the probability of success p
binom.cdf(k, n, p)Calculate the probability to archive k or less successes among n trials with the probability of success p

Task

Here, it would be best if we coped with several tasks.

  1. Calculate the probability that among 50 unique pictures, exactly 5 have a defect; the probability that a picture has a defect is 25%.
  2. Calculate the probability that at least 9(9 or more) employees are satisfied with their salary if we know that there are 20 workers in the project. The probability for the positive answer is 75% .
  3. Calculate the probability that 6 or fewer thefts this month will be revealed; we know that in the specific city, the amount of thefts is 10. The probability of revealing is 5%.

Switch to desktop for real-world practiceContinue from where you are using one of the options below
Section 3. Chapter 4
Switch to desktop for real-world practiceContinue from where you are using one of the options below
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